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A068997 Numbers n such that Sum_{d|n} d*mu(d) divides n. 5
1, 2, 4, 6, 8, 12, 16, 18, 20, 24, 32, 36, 40, 48, 54, 64, 72, 80, 84, 96, 100, 108, 120, 128, 144, 160, 162, 168, 192, 200, 216, 240, 252, 256, 272, 288, 312, 320, 324, 336, 360, 384, 400, 432, 440, 480, 486, 500, 504, 512, 544, 576, 588, 600, 624, 640, 648 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The only squarefree terms so far are a(1), a(2), and a(4). - Torlach Rush, Dec 04 2017
There is a surjective mapping from all even numbers not in this sequence to terms of the sequence. The first such is 10 to a(9). The next is 14,28,42 to a(19). All even numbers not in the sequence are divisors of some term in the sequence. - Torlach Rush, Dec 08 2017
LINKS
FORMULA
n such that A023900(n) divides n.
MAPLE
with(numtheory): A068997 := i->`if`(i mod phi(mul(j, j=factorset(i)))=0, i, NULL): seq(A068997(i), i=1..650); # Peter Luschny, Nov 02 2010
MATHEMATICA
Select[Range[650], Divisible[#, DivisorSum[#, # MoebiusMu[#] &]] &] (* Michael De Vlieger, Nov 20 2017 *)
PROG
(PARI) for(n=1, 1000, if(n%sumdiv(n, d, moebius(d)*d)==0, print1(n, ", ")))
(Haskell)
a068997 n = a068997_list !! (n - 1)
a068997_list = filter (\x -> mod x (a173557 x) == 0) [1..]
-- Reinhard Zumkeller, Jun 01 2015
CROSSREFS
Cf. A173557.
Sequence in context: A124240 A320580 A325763 * A293928 A067712 A060765
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Apr 07 2002
STATUS
approved

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Last modified June 2 22:56 EDT 2023. Contains 363102 sequences. (Running on oeis4.)